[Eoas-seminar] [Seminar-announce] Scientific Computing Colloquium with Jue Yan

[eoas-seminar at lists.fsu.edu]

"Conservative cell-average-based neural network method for nonlinear conservation laws"

Jue Yan
Department of Mathematics
Iowa State University

Please feel free to forward/share this invitation with other groups/disciplines that might be interested in this talk/topic. All are welcome to attend.

NOTE: In-person attendance is requested in our 499 Dirac Science Library (DSL) Seminar Room. Zoom access is intended for external (non-departmental) participants only.


https://fsu.zoom.us/j/94273595552
Meeting # 942 7359 5552


🎦 Colloquium recordings will be made available here, https://www.sc.fsu.edu/colloquium<https://nam04.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.sc.fsu.edu%2Fcolloquium&data=05%7C02%7Csc-seminar-announce%40lists.fsu.edu%7C0c3f58b9813b41e3654208de8db71c26%7Ca36450ebdb0642a78d1b026719f701e3%7C0%7C0%7C639104014737449293%7CUnknown%7CTWFpbGZsb3d8eyJFbXB0eU1hcGkiOnRydWUsIlYiOiIwLjAuMDAwMCIsIlAiOiJXaW4zMiIsIkFOIjoiTWFpbCIsIldUIjoyfQ%3D%3D%7C0%7C%7C%7C&sdata=oYM6oMy4brNJogzu2jINB6UNBsfIscb0uoOl4%2FkehG4%3D&reserved=0>


Wednesday, Apr 1, 2026, Schedule:

* 3:00 to 3:30 PM Eastern Time (US and Canada)
☕ Nespresso & Teatime - 417 DSL Commons

* 3:30 to 4:30 PM Eastern Time (US and Canada)
🕟 Colloquium - 499 DSL Seminar Room


Abstract:
In this talk, we present the recently developed Cell-Average-Based Neural Network (CANN) for time-dependent PDEs. Spatial and temporal discretization in conventional methods is replaced by training a simple feedforward network to obtain an explicit one-step finite volume method. The well-trained network parameters function as the scheme coefficients. The network method has a minimum number of unknowns, which can be quickly trained on a small training dataset. Unlike conventional numerical methods, the CANN approach is not limited by the CFL conditions, enabling the use of significantly larger time steps. This leads to a highly efficient computational method for solving PDEs. The conservative version of the CANN method for nonlinear conservation laws will be discussed. The method, trained on the smooth-solution data from ONE initial-value problem, is verified to solve any initial-value problem involving shocks and rarefaction waves. The network can accurately learn a numerical flux, such as the Lax-Friedrichs flux, thereby guaranteeing convergence to the physically relevant entropy solutions. The extension of the method to non-uniform meshes will be considered. A bound-preserving version of the network method is presented for linear Advection equations.


Additional colloquium details can be found here.
https://www.sc.fsu.edu/news-and-events/colloquium/1915-colloquium-with-jue-yan-2026-04-01<https://nam04.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.sc.fsu.edu%2Fnews-and-events%2Fcolloquium%2F1915-colloquium-with-jue-yan-2026-04-01&data=05%7C02%7Csc-seminar-announce%40lists.fsu.edu%7C0c3f58b9813b41e3654208de8db71c26%7Ca36450ebdb0642a78d1b026719f701e3%7C0%7C0%7C639104014737469887%7CUnknown%7CTWFpbGZsb3d8eyJFbXB0eU1hcGkiOnRydWUsIlYiOiIwLjAuMDAwMCIsIlAiOiJXaW4zMiIsIkFOIjoiTWFpbCIsIldUIjoyfQ%3D%3D%7C0%7C%7C%7C&sdata=NZu29stigp0Dnb37m2%2BCcFCesj%2BrrHVFt2FKKnj2AjE%3D&reserved=0>
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